# Gradient boosting for extreme quantile regression

arXiv: https://arxiv.org/abs/2103.00808 · HTML: https://mlsanity.com/paper/2103.00808/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2021.

## Built on by (most cited first, 17 of 17)

- [Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Risk](https://mlsanity.com/paper/2208.07590/) (2022)
- [Validating Deep Learning Weather Forecast Models on Recent High-Impact Extreme Events](https://mlsanity.com/paper/2404.17652/) (2024)
- [Regression modelling of spatiotemporal extreme U.S. wildfires via partially-interpretable neural networks](https://mlsanity.com/paper/2208.07581/) (2022)
- [Does your graph need a confidence boost? Convergent boosted smoothing on graphs with tabular node features](https://mlsanity.com/paper/2110.13413/) (2021)
- [On Regression in Extreme Regions](https://mlsanity.com/paper/2303.03084/) (2023)
- [Progression: an extrapolation principle for regression](https://mlsanity.com/paper/2410.23246/) (2024)
- [Extreme Conformal Prediction: Reliable Intervals for High-Impact Events](https://mlsanity.com/paper/2505.08578/) (2025)
- [Improving probabilistic forecasts of extreme wind speeds by training statistical post-processing models with weighted scoring rules](https://mlsanity.com/paper/2407.15900/) (2024)
- [Quantile deep learning models for multi-step ahead time series prediction](https://mlsanity.com/paper/2411.15674/) (2024)
- [From Point to probabilistic gradient boosting for claim frequency and severity prediction](https://mlsanity.com/paper/2412.14916/) (2024)
- [Modelling and simulating spatial extremes by combining extreme value theory with generative adversarial networks](https://mlsanity.com/paper/2111.00267/) (2021)
- [Data-driven rainfall prediction at a regional scale: a case study with Ghana](https://mlsanity.com/paper/2410.14062/) (2024)
- [Reliable Real-Time Value at Risk Estimation via Quantile Regression Forest with Conformal Calibration](https://mlsanity.com/paper/2602.01912/) (2026)
- [Robust and Reliable AI for Predictive Quality in Semiconductor Materials Manufacturing with MLOps and Uncertainty Quantification](https://mlsanity.com/paper/2605.07752/) (2026)
- [Stop Suppressing the Tail: Causal Inference for Extreme Events](https://mlsanity.com/paper/2605.27474/) (2026)
- [Gradient boosting for extremes: sampling theory and application to insurance](https://mlsanity.com/paper/2606.14268/) (2026)
- [Convolution Smoothed Quantile Regression for XGBoost](https://mlsanity.com/paper/2608.15290/) (2026)

## Abstract (arXiv)

Extreme quantile regression provides estimates of conditional quantiles outside the range of the data. Classical quantile regression performs poorly in such cases since data in the tail region are too scarce. Extreme value theory is used for extrapolation beyond the range of observed values and estimation of conditional extreme quantiles. Based on the peaks-over-threshold approach, the conditional distribution above a high threshold is approximated by a generalized Pareto distribution with covariate dependent parameters. We propose a gradient boosting procedure to estimate a conditional generalized Pareto distribution by minimizing its deviance. Cross-validation is used for the choice of tuning parameters such as the number of trees and the tree depths. We discuss diagnostic plots such as variable importance and partial dependence plots, which help to interpret the fitted models. In simulation studies we show that our gradient boosting procedure outperforms classical methods from quantile regression and extreme value theory, especially for high-dimensional predictor spaces and complex parameter response surfaces. An application to statistical post-processing of weather forecasts with precipitation data in the Netherlands is proposed.